WASHINGTON — A trio of Republican senators has introduced legislation to allow young people brought to the United States by their parents illegally to receive legal residency if they seek higher education or enlist in the military.

The measure, sponsored by Senators Kay Bailey Hutchison of Texas, Jon Kyl of Arizona, and John McCain of Arizona, would offer a Republican alternative to the so-called Dream Act, providing a pathway to permanent residency — but not citizenship — to young adults who have completed military service or higher education and have worked at least four years.

It would not provide any special path to citizenship for such immigrants.

The proposal comes as an increasing number of Republican voices have called for the party to soften its hard-line opposition to illegal immigration following massive November electoral losses driven, in part, by poor performance with Latino voters.

Hutchison and Kyl insisted that their bill was not a response to the election results. Instead, they said it represented a year of behind-the-scenes work to come up with an alternative to the Dream Act that would allow such young people to remain in the United States without allowing them, as Kyl said, ‘‘to jump ahead of anybody in the citizenship path.’’

Hutchison and Kyl said they were moving ahead with the legislation now so that it could get a public airing before they leave the Senate when its term concludes this year. However, they said they were not optimistic about the chances for movement on the issue during Congress’s ongoing lame-duck session, given the fiscal issues that will occupy most of lawmakers’ time in coming weeks.

The measure, dubbed the Achieve Act, would extend a new visa to people younger than 28 who were brought to the United States before age 14. It would be available to those without serious criminal records and who agree not to access government benefits, including federal student loans.

The visa would allow young people to complete schooling or military service. It could then be transferred, first to a work visa and then, after four years, to a visa allowing for permanent legal residency.

Though the group said they have held productive conversations with Senator Marco Rubio, Republican of Florida, who has been working on his own alternative to the Dream Act and has become a leading voice within the GOP on immigration overhaul, they indicated that he was not prepared to sign on as a cosponsor.

The measure was also introduced without Democratic sponsors, despite repeated calls from Democrats for Republicans to work on bipartisan immigration legislation.

Kyl — who held a joint news conference with Hutchison on Tuesday to unveil the proposal — offered harsh words for President Obama for his June decision to declare that his administration would stop seeking to deport those who would have qualified under the Dream Act.

‘‘The administration has unfortunately chosen . . . to take the law into its own hands, choosing to ignore current law because it didn’t think it was good policy,’’ Kyl said. ‘‘Those of us who strongly believe in the rule of law believe that in our country, if you don’t like the law, change it, or seek to change it. Don’t violate it.’’

Though the proposal will most likely be dismissed by some in the Republican camp for offering amnesty to illegal immigrants, a senior Democratic aide, who is not authorized to speak publicly about still-evolving legislation, suggested that the retiring Republicans should be given little credit for advancing the idea on the eve of their departure from the Senate.

‘‘It’s not exactly a profile in courage for two senators — who happen to turn into pumpkins in about a month — to weigh in on a bill that’s been around for a decade and that they’ve opposed for nearly as long,’’ he said. ‘‘It’ll be interesting to see if members of their party will be willing to continue the conversation they’ve waited far too long to start.’’